International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 87808, 9 pages
doi:10.1155/2007/87808
Dunkl translation and uncentered maximal operator on the real line
Chokri Abdelkefi1
and Mohamed Sifi2
1Department of Mathematics, Preparatory Institute for Engineering Studies of Tunis, Monfleury, Tunis 1089, Tunisia
2Department of Mathematics, Faculty of Sciences of Tunis, Tunis-El Manar University, Tunis 1060, Tunisia
Abstract
We establish estimates of the Dunkl translation of the characteristic function χ[−ɛ,ɛ], ɛ>0, and we prove that the uncentered maximal operator associated with the Dunkl operator is of weak type (1,1). As a consequence, we obtain the Lp-boundedness of this operator for 1<p≤+∞.